Most Helpful Girl
Guys making the first move is an extremely well established social norm, and therefore difficult to change.
Also, I personally would not feel comfortable initiating contact because some guys will without a doubt act as if you owe them something for making that move.1
Most Helpful Guy
Because girls want a confident guy. Confident guys approach whereas unconfident ones do not. Confident guys also don't look for 'signs' they assume the girl will be attracted.
If a girl approaches there's a risk he doesn't like her so by not doing so she avoids being rejected and being seen as a slut (if she's self conscious about that)0